found by Majda [1]} (and written in our notations) for shock waves in isentropic gas dynamics. It was shown in [2]} that \(\mathcal {D}>0\) . Comparing (REF ) and (REF ), this means that the elastic force plays stabilizing role. Moreover, it was proved in [2]} that \(\widetilde{M}^2(R-1)<1\)  for compressive shock waves (\(R>1\) ) with convex equations of state \(p=p(\rho )\) . This implies that these shock waves are uniformly stable because (REF ) holds for them. By the way, the rarefaction shock waves (\(R<1\) ) are also always uniformly stable, cf. (REF ).
